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In the classification of crystals, each point group defines a so-called (geometric) crystal class. There are infinitely many three-dimensional point groups. However, the crystallographic restriction on the general point groups results in there being only 32 crystallographic point groups.
The main classes of point groups are C, D, S, T, O, and I. The first two classes are most common. Each of these classes is subdivided into different point groups. Compounds in the C class can be Cs, Ci, Cn, Cnv, or Cnh, where n is an integer.
A Point Group describes all the symmetry operations that can be performed on a molecule that result in a conformation indistinguishable from the original. Point groups are used in Group Theory, the mathematical analysis of groups, to determine properties such as a molecule's molecular orbitals.
point group, also called Crystal Class, in crystallography, listing of the ways in which the orientation of a crystal can be changed without seeming to change the positions of its atoms.
Assigning Point Groups Determine if the molecule is of high or low symmetry. If not, find the highest order rotation axis, Cn. Determine if the molecule has any C2 axes perpendicular to the principal Cn axis. If so, then there are n such C2 axes, and the molecule is in the D set of point groups.
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Assigning Point Groups Determine if the molecule is of high or low symmetry. If not, find the highest order rotation axis, Cn. Determine whether the molecule has any C2 axes perpendicular to the principal Cn axis. ... Determine whether the molecule has a horizontal mirror plane (\u03c3h) perpendicular to the principal Cn axis.
In geometry, a point group is a mathematical group of symmetry operations (isometries in a Euclidean space) that have a fixed point in common. The coordinate origin of the Euclidean space is conventionally taken to be a fixed point, and every point group in dimension d is then a subgroup of the orthogonal group O(d).
In the classification of crystals, each point group defines a so-called (geometric) crystal class. There are infinitely many three-dimensional point groups. However, the crystallographic restriction on the general point groups results in there being only 32 crystallographic point groups.
In the classification of crystals, each point group defines a so-called (geometric) crystal class. There are infinitely many three-dimensional point groups. However, the crystallographic restriction on the general point groups results in there being only 32 crystallographic point groups.
We now return to the concept of stereographic projections to illustrate the symmetry elements of the 32 crystallographic point groups. The figure below shows a ball & stick figure of a water molecule viewed down the twofold rotation axis that passes through the central oxygen atom.

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